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Evaluation of WRF performance for the analysis of surface wind speeds over various Greek regions
Get PDFIn this study we analyze the surface wind variability over selected areas of the Greek territory by comparing a 3-Km spatial resolution simulation performed with the Weather Research and Forecasting (WRF) model for the summer months of 2013 with actual surface measurements. Daily 36hrs runs at 12 UTC were driven by FLN (1 deg x 1 deg) data for the period of 11 July 2013 to 17 July 2013. Various verification statistics such as BIAS, RMSE and DACC for wind speed and direction were used to gauge the mesoscale model performance
Convergence of variational approximation schemes for three dimensional elastodynamics with polyconvex energy
Get PDFCollapse Transitions in Thermosensitive Multi-block Copolymers: A Monte Carlo Study
Get PDFMonte Carlo simulations are performed on a simple cubic lattice to investigate the behavior of a single linear multiblock copolymer chain of various lengths N. The chain of type (AnBn)m consists of alternating A and B blocks, where A are solvophilic and B are solvophobic and N = 2nm. The conformations are classified in five cases of globule formation by the solvophobic blocks of the chain. The dependence of globule characteristics on the molecular weight and on the number of blocks, which participate in their formation, is examined. The focus is on relative high molecular weight blocks (i.e., N in the range of 500 – 5000 units) and very differing energetic conditions for the two blocks (very good – almost athermal solvent for A and bad solvent for B). A rich phase behavior is observed as a result of the alternating architecture of the multiblock copolymer chain. The comparison among equivalent globules consisting of different number of B-blocks shows that the more the solvophobic blocks constituting the globule the bigger its radius of gyration and the looser its structure. Comparison between globules formed by the solvophobic blocks of the multiblock copolymer chain and their homopolymer analogs highlight the important role of the solvophilic A-blocks
On the confinement of bounded entire solutions to a class of semilinear elliptic systems
Get PDFUnder appropriate assumptions, we show that all bounded entire solutions to a class of semilinear elliptic systems are confined in a convex domain. Moreover, we prove a
Liouville type theorem in the case where the domain is strictly convex. Our result represents
an extension, under less regularity assumptions, of a recent result. We also provide several application
Singular limiting induced from continuum solutions and the problem of dynamic cavitation
Get PDFIn the works of
K.A. Pericak-Spector and S. Spector [Pericak-Spector, Spector 1988, 1997] a class of self-similar
solutions are constructed for the equations of radial isotropic elastodynamics
that describe cavitating solutions. Cavitating solutions decrease the total
mechanical energy and provide a striking example of non-uniqueness of entropy weak solutions
(for polyconvex energies) due to point-singularities at the cavity. To resolve
this paradox, we introduce the concept of singular limiting induced from continuum solution (or slic-solution),
according to which a discontinuous motion is a slic-solution if its averages
form a family of smooth approximate solutions to the problem. It turns out that there is an energetic cost for
creating the cavity, which is captured by the notion of slic-solution but neglected by the
usual entropic weak solutions. Once this cost is accounted for, the total mechanical energy of the
cavitating solution is in fact larger than that of the homogeneously deformed state.
We also apply the notion of slic-solutions to a one-dimensional example describing the onset of fracture,
and to gas dynamics in Langrangean coordinates with Riemann data inducing vacuum in the wave fan
On the XFEL Schroedinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging
Get PDFWe analyse a nonlinear Schr\"odinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree-Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray Free Electron Laser (XFEL). We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schr\"odinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential
A weighted Hardy-Sobolev-Maz’ya inequality
Get PDFWe provide a weighted extension of a Hardy-Sobolev-Maz’ya inequality that is due to Filippas, Maz’ya and Tertikas
Uniform estimates for positive solutions of a class of semilinear elliptic equations and related Liouville and one-dimensional symmetry results
Get PDFWe consider a semilinear elliptic equation with Dirichlet boundary conditions in a smooth, possibly unbounded, domain. Under suitable assumptions, we deduce a condition on the size of the domain that implies the existence of a positive solution satisfying a uniform pointwise estimate. Here, uniform means that the estimate is independent of the domain. The main advantage of our approach is that it allows us to remove a restrictive monotonicity assumption that was imposed in the recent paper. In addition, we can remove a non-degeneracy condition that was assumed in the latter reference. Furthermore, we can generalize an old result, concerning semilinear elliptic nonlinear eigenvalue problems. Moreover, we study the boundary layer of global minimizers of the corresponding singular perturbation problem. For the above applications, our approach is based on a refinement of a useful result, concerning the behavior of global minimizers of the associated energy over large balls, subject to Dirichlet conditions. Combining this refinement with global bifurcation theory and the celebrated sliding method, we can prove uniform estimates for solutions away from their nodal set. Combining our approach with a-priori estimates that we obtain by blow-up, a doubling lemma, and known Liouville type theorems, we can give a new proof of a known Liouville type theorem without using boundary blow-up solutions. We can also provide an alternative proof, and a useful extension, of a Liouville theorem, involving the presence of an obstacle. Making use of the latter extension, we consider the singular perturbation problem with mixed boundary conditions. Moreover, we prove some new one-dimensional symmetry and rigidity properties of certain entire solutions to Allen-Cahn type equations, as well as in half spaces, convex cylindrical domains. In particular, we provide a new proof of Gibbons' conjecture